Radicals and Exponential Functions: math test, Grade 9 – download the PDF

1 Simplifying radicals / 4 pts

Simplify each radical.

1. \(\sqrt{45}\)
2. \(\sqrt{128}\)
3. \(5\sqrt{12}\)
4. \(\sqrt{18}\cdot\sqrt{2}\)

2 Operations with radicals / 4 pts

Simplify each expression.

1. \(7\sqrt{3}-2\sqrt{3}+\sqrt{12}\)
2. \((2+\sqrt{6})(2-\sqrt{6})\)
3. \((\sqrt{3}+4)^2\)

3 Rationalizing / 3 pts

Rationalize each denominator.

1. \(\dfrac{12}{\sqrt{6}}\)
2. \(\dfrac{8}{3-\sqrt{5}}\)

4 A growing app / 3 pts

A calculator is allowed. A streaming app has 8,000 users and grows 15% each month.

1. Write a function \(U(t)\) for the number of users after \(t\) months.
2. How many users are there after 4 months? Round to a whole number.

5 Compound interest / 3 pts

A calculator is allowed. You deposit \(\$2{,}500\) at 3% interest compounded annually for 6 years. Find the final balance and the interest earned, to the nearest cent.

6 Identifying a model / 3 pts

The table shows values of a function.

(a) Is the function linear or exponential? Justify. (b) Write an equation. (c) Find \(y\) when \(x=5\).