Geometry
A rectangle has an area of 96 cm² and a length of 12 cm. What is the width?
96 ÷ 12 = 8 cm
Expand and simplify - (x+3)(x−5)
x^2−2x−15
The triangle lengths are 4cm, 6cm, and 4cm. What kind of triangle is it?
Isosceles
Simplify the expression 4m+5+2m-1
6m+4
Kim had 4 chocolate chip cookies and 3 sugar cookies. Her sister ate 2 of her chocolate chip cookies. How many cookies are left?
5/7
A triangle has angles 40° and 90°. What is the type of triangle and the third angle?
50°, right-angled triangle
Simplify: 4(2x−3)−2(x+5)
8x−12−2x−10=6x−22
A right triangle has legs 6 cm and 8 cm. What is the length of the hypotenuse?
10
Five more than twice an unknown number is 25. What is the unknown number?
n = 10
Bob, Lucy, and Sue want to share seven 600mL drinks between them. How many drinks does each person get?
2 1/3 drinks (1400 mL)
The perimeter of a rectangle is 64 cm. If the length is 20 cm, what is the width?
2L + 2W = 64 → 2×20 + 2W = 64 → W = 12 cm
Solve: (x+4)/2 = (3x-2)/4
4x+16=6x−4
x = 10
A ladder is 5 m long and the base is 3 m from the wall. How high up the wall does the ladder reach?
4 m
The formula for changing degrees Celsius to degrees Fahrenheit is F=59/C+32. Rearrange the formula to make C the subject of the formula.
C = 59/(F - 32)
Mary needs to order pizza for 18 people. If each person should receive 1/4 of a pizza, how many whole pizzas should she order?
A triangle has sides 5 cm, 12 cm, and 13 cm. Is it a right triangle? Show why.
5² + 12² = 25 + 144 = 169 = 13² → Yes, it’s a right triangle
A school sells concert tickets. Child tickets cost $8 and adult tickets cost $12. A total of 10 tickets were sold for $96. How many of each type were sold?
8x+12(10−x)=96→8x+120−12x=96→−4x=−24→x=6
In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is the angle θ?
37 degrees
Sixty more than nine times a number is the same as two less than ten times the number. What is the number?
n = 62
Tom needs to paint his garden fence. The total length of fencing is 15 1/4m. He paints 6 1/2m on Saturday and manages to paint half of the remainder the next day before he runs out of paint. How much fencing does he paint on Sunday?
4 3/8
A compound shape has a rectangle (6 cm × 10 cm) and a semicircle on one short side (diameter 6 cm). What is the total area? (Use π = 3.14)
Rectangle area = 6×10=60 cm²
Semicircle area = ½×π×r2=½×3.14×32= 14.13 cm²
Total area = 60+14.13= 74.13 cm squared
A rectangle has a length of 2x +1 and a width of x−2. Its area is 60 cm2. Find the value of x.
(2x + 1)(x - 2) = 60 → 2x^2 - 3x - 2 = 2x^2 - 3x - 62 = 0 → Solve using quadratic formula or factor method (approx x ≈ 6.5 or x ≈ -4.8)*
A surveyor is measuring for the distance across a small lake. He has set up his transit on one side of the lake 90m from a piling that is directly across from the pier on the other side of the lake. From his transit, the angle between the piling and the pier of 35 degrees. What is the distance between the piling and their pier to the nearest m?
52m
Find three consecutive odd integers such that the sum of the first, two times the second, and three times the third is 70.
9, 11, 13
Sarah, Josh, and Jack are related. Jack is 1/3 of Sarah's age and Tom is 1/4 of Sarah's age. If Josh is five years younger than Jack, how old is Sarah?
60 years old