Summer Math Review (open book, double points if don't use book)

Percentages

100

What is 15% of 80?

12

200

Increase 60 by 25%.

75

300

The price of a jacket is $120. If the price is increased by 15%, what is the new price?

$138

400

An investor bought shares for $2,000. After a year, the value of the shares increased by 12.5%. What is the value of the shares after a year?

$2,250

500

A store sells an item for $75 after applying a 30% markup on the cost price. What was the cost price of the item?

$57.69 (rounded to two decimal places)

Algebraic Expressions

100

Simplify 4x−2(3x−7).

−2x+14

200

Expand (2x−5)(x+4).

2x^2+3x-20

300

Factorize 6x^2 + 11x + 3.

(2x+3)(3x+1)

400

Add 2x/5 + 3x/4.

(8x +15x)/20 = 23x/20

500

Factorize x^2−6x+9.

AND

Simplify (6x^2-7)/3x.

(x−3)(x−3) or (x - 3)^2

AND

2x-4

Algebraic Equations

100

Solve for x: 7x+2=4x+14

x = 4

200

Solve for x: 3(2x−1)=15

x=3

300

Solve the simultaneous equations:

3x - y = 4

2x + y = 7

x=2, y=3

400

Solve for x: x²−16=0

x = 4, x = -4

500

Solve for x: 2x²−3x−2=0

AND

5x + 2y = 12

3x + 4y = 10

x=2, x=-½

AND

x=1.6, y=0.4

Indices (Exponents)

100

(-2)³

-8

200

(3²)³

3⁶=729

300

Simplify 4⁵/4²

AND

7^-2

4³=64

AND

1/49

400

27^2/3

AND

(5² x 5^-4) / 5^-3

9

AND

5^-2/5^-3=5¹=5

500

(27x³)^⅔ 

9x²

Coordinate Geometry

100

Find the gradient of the line that passes through the points A(1,2) and B(4,5).

1

200

Find the gradient of the line that passes through the points A(−3,−7) and B(4,5).

12/7

300

Find the length of the line segment between points A(0,0) and B(7,24).

25

400

Find the midpoint of the line segment between points A(−2,5) and B(4,−1).

(1,2)

500

Find the gradient, length, and midpoint of the line segment between points A(−5,4) and B(7,−8).

gradient: -1

length: 12 square root of 2

midpoint: (1, -2)