Factors and primes
List the first five prime numbers.
2, 3, 5, 7, 11
Write the answer to this calculation in index form.
128 ÷ 125
123
Solve -42 ÷ 7
-6
Expand 2a(3 - b)
6a - 2ab
List all integers of x for the inequality -3 ≤ x < 2
-3, -2, -1, 0, 1
Write 84 as a product of prime factors.
84=22x3x7
Solve ∛729 + 52
∛729 + 52
=9 + 25
=34
Solve 46 - (6 + 3) x 4
46 - (6 + 3) x 4
=46 - 9 x 4
=46 - 36
=10
Expand -6h(4k - 7h)
-24kh + 42h2
Round 5643 to 1s.f.
6000
Write 456 as a product of prime factors.
456=23x3x19
Solve
(34)5 ÷ 320
30 or 1
Find the value of x, given
x ÷ 5 - 9 = 2
x ÷ 5 - 9 = 2
x ÷ 5 = 2 + 9
x ÷ 5 = 11
x = 11 x 5
x = 55
Factorise 45n3 + 30n
15n(3n2 + 2)
Round 2.0455 to 2s.f.
2.0
Given the following numbers and their prime factors, find their HCF:
360=23x32x5
144=24x32
HCF=23x32
=72
Solve x3 + 216 = 0
x3 + 216 = 0
x3 = -216
x = ∛ -216
x = -6
Solve 4x2 + 5x - 18 when x = -3
4x2 + 5x - 18
= 4(-3)2 + 5(-3) - 18
= 4(9) + 5(-3) - 18
= 36 - 15 - 18
= 3
Factorise 6xy - 22y2 + 18yz
2y(3x - 11y + 9z)
Given that 1 kilometer = 0.621371192 miles, find the distance in miles for 6 kilometers rounded to 3s.f.
0.621371192 x 6 = 3.728227153
= 3.73 miles
Given the following numbers and their prime factors, find their LCM:
132=22x3x11
126=2x32x7
LCM=22x32x7x11
=2772
Given that 1936 = 24 x 112,
write √1936 as a product of prime factors.
√1936 = 22 x 11
Given that a triangle has a base of 4y and a height of 3y, write an expression for the area of the triangle.
Area of triangle = 3y x 4y x 1/2
= 12y2 x 1/2
= 6y2
Simplify b(3b + 5c) - 2c(6b - 4c)
b(3b + 5c) - 2c(6b - 4c)
=3b2 + 5bc - 12bc + 8c2
=3b2 - 7bc + 8c2
Given that the gravitational acceleration on Earth, gEarth is 9.80665 m/s2 and the gravitational acceleration on Mars is one third of Earth's, find gMars rounded to 3s.f.
gMars = 9.80665 ÷ 3
= 3.268883333
= 3.27 m/s2 (3s.f.)