Algebraic Language
What is the term for a letter that represents an unknown number?
Pronumerals
If x = 2 and y = 5, what is the value of x + y?
x + y = 2 + 5 = 7
Simplify the expression 7a + 2a.
9a (Like Terms)
What is the name of the straight line that passes through the centre of a circle and touches both sides?
Diameter
State the formula used to find the circumference of a circle if you know the diameter.
C = πd
Rewrite the expression 5 × a × a without using the multiplication symbol.
5a2
If a = 3, evaluate 2a2 + 3
2 × a × a + 3
= 2 × 3 × 3 + 3
= 18 + 3
= 21
Simplify 5x − 2xy + 7x + 4y by collecting like terms.
12x − 2xy + 4y
If the radius of a circle is 6.5 cm, what is its diameter?
6.5 x 2 =13
Calculate the circumference of a circle with a diameter of 15 cm (Round to 1 decimal place)
47.1 cm
In the expression 2x − 3y − 5, which term is the "constant"?
−5
If a = 3 and b = -2, evaluate -2a3 - 4b
(-2) × a3 - 4 × b
= (-2) × 33 - 4 × (-2)
= (-2) × 27 + 8
= -54 + 8
= -46
What is the result of multiplying 4a × (-2ab)?
-8a2b
Define "Pi" (π) in terms of a circle's circumference (C) and diameter (d).
Pi is the quotient of the circumference to the diameter (C/d)
Find the circumference of a circle with a radius of 9 cm (Leave your answer in the exact form)
2 x pi x radius
2 x pi x 9
18pi or 18π
Write an algebraic expression for the following: "The sum of m and n, divided by 2."
(m + n) ÷ 2 or (m + n) /2
The formula for the total surface area of a specific cylinder (without a top) is given by S = πr2 + 2πrh. Use your calculator to find the value of S when the radius (r) is 4 and the height (h) is 10.
Correct to the nearest whole number.
S = πr2 + 2πrh
S = π x 4 x 2 + 2 x π x 4 x 10
S = 88π = 276.4601535
S = 276 (whole number)
Simplify 0.5a2 × 8a3
4a5
Is a 'diameter' also a 'chord'?
Explain why?
A chord joins any two points on the circumference; a diameter is a special chord that must pass through the centre.
Calculate the perimeter of a sector with a radius of 8 cm and an arc length of 12.6 cm
28.6 cm (Calculated as 12.6 + 8 + 8)
Rewrite the expression (3t2 − 4) / (x2 − 2y) using the division (÷) and multiplication (×) symbols.
Hint: / means over
(3 × t × t − 4) ÷ (x × x − 2 × y)
A technician uses the formula V = u2 + 2as to find the final velocity of an object. Find the value of V if u = 8, a = −3, and s = 10.
Solution: V = (8)2 + 2 x (−3) x (10)
= 64 + (−60)
= 64 − 60
= 4
Find the area of a rectangle with length 4xy and width 2yx.
Area of the rectangle = L x W
= 4xy x 2yx
= 8x2y2
If a circle has a circumference of 31.4 cm, and you draw a chord that is exactly 10 cm long and passes through the center of the circle, what is the specific name of this chord and what is the length of the radius?
The chord is the Diameter.
Since the diameter is 10 cm, the radius is 5 cm.
A circular pool has a diameter of 15 m and a fence is placed 1 m away from its edge. What is the radius of the fence?
8.5 m (Pool radius 7.5 m + 1 m gap)