Number and Algebra

Write the value of $(2 \times 10^{3})^{2}$ in standard form.

If a recipe requires $250$ g of flour and you use $260$ g, what is the absolute error?

A cube has a side length of $2$ cm. Calculate its volume in m$^{3}$.

Round $4.995$ to $2$ decimal places.

A bank offers an exchange rate of 1 AUD = 0.90 SGD. There is a flat fee of 10 AUD for any transaction. How many SGD will you get for 200 AUD?

A calculation gives a result of $25.467$. If this is rounded to the nearest whole number, calculate the percentage error relative to the original value.

Round the number $999.99$ to three significant figures.

Convert a speed of $90$ km/h to meters per second (m/s) and express the answer to three significant figures.

A person saves USD 200 at the end of every month in an account paying $3.6\%$ nominal annual interest compounded monthly. How much is in the account after 10 years, to the nearest dollar?

A bacteria culture doubles every 4 hours. If there are 1000 bacteria initially, how many will there be after 24 hours?

Calculate $(4 \times 10^{-2}) \div (8 \times 10^{-5})$ and express the result in scientific notation.

The diameter of the dwarf planet Pluto is $2,376$ km. Write this in scientific notation.

Evaluate $1 \div (2 \times 10^{3})$ and express the result in scientific notation.

Calculate $2.2 \times 10^{4} \times 3 \times 10^{-2}$ and express the result in scientific notation.

A GDC output is $9.998E8$. When rounded to three significant figures, what is this value in scientific notation?

Calculate $(8 \times 10^{-4}) \times (5 \times 10^{-3})$ and express the result in scientific notation.

A small region has an area of $0.05$ square kilometers. Express this area in square meters using scientific notation.

A galaxy contains approximately $2.0 \times 10^{11}$ stars. If each star has an average mass of $1.5 \times 10^{30}$ kg, calculate the total mass of the stars in the galaxy in scientific notation.

The pH of a solution is calculated using $[H^+] = 10^{-pH}$. If a solution has a pH of 8.4, calculate the hydrogen ion concentration $[H^+]$ in scientific notation.

A micro-meteorite has a mass of $3.5 \times 10^{-9}$ kg. If $4.0 \times 10^7$ of these hit a satellite, calculate the total mass added to the satellite in grams.

A savings account balance increases from $2000 to$2120 over a year. Calculate the annual percentage interest rate.

An athlete's weight decreased from $80$ kg to $76$ kg. Calculate the percentage decrease in their weight.

During a sale, a $400$ washing machine is sold for $340$. Calculate the percentage discount.

A tank is $65\%$ full. If it contains $1300$ liters of water, what is the total capacity of the tank?

An account grows from USD 5000 to USD 5125 in one month. Calculate the monthly percentage growth rate.

A rectangle has a length of 8 cm and a width of 5 cm. If both dimensions are increased by 20%, what is the percentage increase in the area?

A shirt is originally priced at USD 40. It is on sale for USD 32. Calculate the percentage discount.

The diameter of a circle is measured with a $4\%$ error. Calculate the percentage error in the calculated area of the circle.

A student measures the mass of an object as $0.450$ kg. The actual mass is $0.455$ kg. Calculate the absolute value of the percentage error to three decimal places.

The price of a book is $P$. It is increased by $20\%$ and then the new price is decreased by $20\%$. The final price is 19.20 USD. Find the original price $P$.

Which of the following numbers is the largest?

Simplify $\frac{x^7 \cdot x^{-3}}{x^2}$.

If $f(x) = 4^x$, find the value of $f(2.5)$ using your GDC.

Calculate $10^{-1} + 10^0$.

If $4^x = 8^{y}$, what is the ratio of $x$ to $y$?

Calculate the value of $\frac{8 \times 10^5}{4 \times 10^{-2}}$.

A city's population increases from 100,000 to 150,000 in 10 years. Assuming exponential growth, what is the annual growth rate $r$?

A rectangular sheet has dimensions $2.4 \times 10^{-2} \text{ m}$ by $1.5 \times 10^{-3} \text{ m}$. Find the area of the sheet in square millimeters.

A population is modeled by $P(t) = A \cdot B^t$. If $P(0) = 500$ and $P(2) = 720$, find the value of $P(5)$ to the nearest integer.

The power $P$ in a circuit is given by $P = I^2 R$. If $I = 4.0 \times 10^{-3} \text{ Amperes}$ and $R = 5.0 \times 10^5 \text{ Ohms}$, calculate $P$ in Watts.

Calculate the $20^{th}$ term of an arithmetic sequence where $u_1 = 100$ and $d = -5$.

What is the common difference $d$ for the sequence $1, 1.5, 2, 2.5, ...$?

If $u_n = 3 \times 2^{n-1}$, find $u_4$.

A person deposits 100 each month into a safe (no interest). How much is in the safe after 2 years?

An investment triples in value over 15 years. What is the annual compound interest rate?

A ball is dropped and each bounce reaches 75% of the height of the previous bounce. If the first bounce reaches 1.5 m, find the height of the 6th bounce to the nearest centimeter.

A sequence is given by $u_n = 4n - 3$. Calculate the sum of terms from $u_{10}$ to $u_{20}$ inclusive.

If $\sum_{r=1}^{n} 3(1.2)^{r-1} = 111.45$, find the value of $n$ to the nearest integer.

A ball is dropped from 5 meters. Each bounce it loses 15% of its previous height. Find the height of the ball on its 10th bounce.

Find the common difference of an arithmetic sequence where $u_{1} = 10$ and $S_{20} = 670$.

Which of the following values of $d$ would make the arithmetic sequence $10, 10+d, 10+2d, \dots$ decreasing?

Find the sum $S_n$ for the sequence $10, 8, 6, \dots$ when $n=10$.

In an arithmetic sequence $u_k = 2k - 5$. Find $u_{20}$.

A debt of 1000 dollars is repaid by paying 50 dollars in the first month and increasing the payment by 10 dollars each month. How much is paid in the $6^{th}$ month?

An arithmetic sequence has a first term of 100 and a common difference of $-5$. Find the sum of all the positive terms in the sequence.

A person saves 200 in the first month and increases the monthly saving by 25. Find the total amount saved after 3 years.

An office building has 15 floors. The ground floor is 5 meters high, and every floor above it is 3.5 meters high. Find the total height to the top of the 15th floor.

Find the common difference $d$ of an arithmetic sequence where $u_1 = 5$ and $S_{20} = 4u_{10} + 190$.

A farmer produces 200 eggs on the first day. Each day, production increases by a constant amount. If the total production after 30 days is 7500 eggs, how many eggs were produced on the 30th day?

A subscription service costs 10 in the first month and increases by 1.50 each month. Find the total cost after 2 years.

A geometric sequence has terms $u_1 = a, u_2 = ar, u_3 = ar^2$. If $a=10$ and $r=0.1$, find $u_3$.

A ball rebounds to a height of $h_n = 20 \times (0.6)^n$ meters after the $n^{th}$ bounce. What is the height after the $1^{st}$ bounce?

In a geometric sequence, $u_n = 3 \times (-1)^{n-1}$. What is the sum of the first $4$ terms?

Find the common ratio $r$ if $u_1 = 500$ and $u_2 = 450$.

A geometric sequence has terms $u_1 = 2$, $u_2 = 6$, $u_3 = 18$. Find $S_7 - S_6$.

A ball is dropped from a height of 10 m. On each bounce, it reaches 80% of its previous height. Calculate the total vertical distance traveled (up and down) by the ball during the first 3 bounces (i.e. from the drop until it hits the ground for the 4th time).

Find the common ratio $r$ of a geometric sequence where $u_2 = 10$ and $u_4 = 6.4$.

Find the sum of the first 15 terms of the geometric sequence where $u_1 = 100$ and $r = 0.9$, to the nearest integer.

A car was worth USD 20000 in 2015 and USD 12800 in 2017. Assuming the value follows a geometric sequence, find the common ratio $r$.

The fifth term of a geometric sequence is 48 and the sixth term is 96. Find the sum of the first 10 terms.

A TV costs USD 800 and its value depreciates by $25\%$ each year. What is its value after 2 years?

If an investment of USD 100 grows to USD 110 in one year, what is the annual compound interest rate (compounded annually)?

A person invests USD 200 a month for 10 years. How many total payments are made?

A bank pays $3.6\%$ nominal annual interest compounded monthly. What is the effective annual interest rate?

If you invest 100 USD at the end of every month at an annual interest rate of 6% compounded monthly, how many months will it take for the balance to reach 5000 USD?

A equipment item depreciates from 8000 EUR to 2000 EUR in 5 years. Find the constant annual percentage rate of depreciation.

An investment of 7000 USD is made at 4.5% interest compounded semi-annually. How much will the investment be worth after 10 years?

If you invest 100 USD at the end of each year for 10 years at 5% interest compounded annually, and then leave the final balance to grow for another 5 years with the same interest rate but no further deposits, what is the final amount?

A car's value $V$ in dollars after $t$ years is modeled by $V = A e^{-kt}$. If the car is worth 30000 USD when new and 15000 USD after 4 years, find the value of $k$ to four decimal places.

A 10-year bond with a face value of 10000 USD pays 5% annual coupons (at the end of each year). If an investor buys the bond and reinvests each coupon in an account paying 3% compounded annually, calculate the total value of the coupons and their interest after 10 years.

An amount of 1500 USD is invested at $4\%$ compound interest per annum. Calculate the total value after 5 years, compounded annually.

How much interest is earned on 5000 USD at $3\%$ per annum compounded quarterly for 6 months?

Calculate the principal that would grow to 1100 USD in 2 years at a $5\%$ simple interest rate.

A camera costs 800 USD and depreciates by $20\%$ each year. Find its value after 2 years.

Find the future value of 2000 invested at $2.5\%$ per annum compounded annually for 10 years.

Calculate the interest on 10000 at $5\%$ simple interest for 4 months.

A stock's value decreased by $10\%$ in the first year and increased by $10\%$ in the second year. If the initial value was 100, find the value after 2 years.

A sum of money is invested at $5\%$ p.a. compounded annually. If the interest earned in the second year is 105, find the original sum invested.

A loan of 2500 is taken at $12\%$ p.a. simple interest. If the total amount to be repaid is 4300, find the duration of the loan in years.

An investment of 4500 is made at $3.5\%$ p.a. compounded quarterly. Find the value after 10 years.

A 200000 mortgage at 4% p.a. compounded monthly for 30 years has a monthly payment of 954.83. If the term was 15 years instead, the monthly payment would be 1479.38. How much less interest is paid in the 15-year mortgage?

If a loan's interest rate increases while the term and principal stay the same, which of the following happens?

A loan of 5000 is taken at 9% p.a. compounded monthly for 3 years. Calculate the total amount repaid.

Zane borrows 12000 at 5% p.a. compounded monthly. He wants to pay off the loan in 4 years. What value should be entered for $FV$ in the TVM solver to find the monthly payment?

A student takes a 15,000 USD loan at 3% interest compounded monthly. They agree to pay 300 USD per month. What is the outstanding balance after 3 years?

A 50,000 GBP loan is taken for 10 years at 4.2% interest compounded monthly. If the borrower wants to reduce the total interest paid by 2,000 GBP, how much extra should they pay each month (rounded to the nearest pound)?

A person borrows 12,000 AUD at 7.2% annual interest compounded monthly for 4 years. What is the total interest paid in the last year of the loan?

A loan of 100,000 USD has an interest rate of 4.5% compounded monthly. If the monthly payment is set at 600 USD, calculate the balance after 10 years.

A 10,000 EUR loan at 8% compounded monthly is repaid with monthly payments of 250 EUR. Calculate the total number of payments, where the final payment might be less than 250 EUR.

A property is bought for 450,000 AUD. A 20% deposit is paid. The mortgage is at 3.2% compounded monthly for 25 years. Calculate the total interest paid over the 25 years as a percentage of the mortgage amount.

An industrial fan costs 850 and depreciates at 9% per year. Find its value after 2 years.

A projection system costs 5,500 and depreciates at 20% per year. Find its value after 3 years.

A new electric bike costs 3,800 and depreciates at 12% per year. Find the value after 3 years to the nearest dollar.

A security system costs 2,400 and depreciates at 15% per year. Find the total value lost after 2 years.

A machine bought for 10,000 USD depreciates by $r\%$ each year. After 3 years, its value is 5,120 USD. Find the value of $r$.

An office chair costs 300 USD and depreciates linearly at 30 USD per year. Find its value after 4 years.

A car worth 20,000 USD depreciates at a rate of 10% per year. Find the total depreciation after 3 years.

An asset worth 75,000 depreciates at 12% per year. What is the difference between the depreciation amount in year 4 and the depreciation amount in year 5?

A machine has a current value of 24,000. If it has been depreciating at 15% per year for the last 2 years, what was its value 2 years ago?

An electric car battery has a capacity of 100 kWh. It loses 2.5% of its remaining capacity every year. What is its capacity after 8 years?

1. Annuities (HL): practice question 1 for Number and Algebra?

1. Annuities (HL): practice question 2 for Number and Algebra?

1. Annuities (HL): practice question 3 for Number and Algebra?

1. Annuities (HL): practice question 4 for Number and Algebra?

1. Annuities (HL): practice question 5 for Number and Algebra?

1. Annuities (HL): practice question 6 for Number and Algebra?

1. Annuities (HL): practice question 7 for Number and Algebra?

1. Annuities (HL): practice question 8 for Number and Algebra?

1. Annuities (HL): practice question 9 for Number and Algebra?

1. Annuities (HL): practice question 10 for Number and Algebra?

1. Binomial theorem (HL): practice question 1 for Number and Algebra?

1. Binomial theorem (HL): practice question 2 for Number and Algebra?

1. Binomial theorem (HL): practice question 3 for Number and Algebra?

1. Binomial theorem (HL): practice question 4 for Number and Algebra?

1. Binomial theorem (HL): practice question 5 for Number and Algebra?

1. Binomial theorem (HL): practice question 6 for Number and Algebra?

1. Binomial theorem (HL): practice question 7 for Number and Algebra?

1. Binomial theorem (HL): practice question 8 for Number and Algebra?

1. Binomial theorem (HL): practice question 9 for Number and Algebra?

1. Binomial theorem (HL): practice question 10 for Number and Algebra?