Page 1
1)
a) 11a
b) 4a + 3b + 5a = 9a + 3b
c) 5a + 2b - 2a = 3a + 2b
d) 4x + 3y + 2x - 4y = 6x - y
e) 3p - 4p + 7p = 6p
f) x² + y + 3x² + 3y = 4x² + 4y
g) 4x² + 3x + 2x² + 6x = 6x² + 9x
h) 3p² + q - 4p² + 2q = -p² + 3q
2)
a) 3x + 21
b) 6x - 12
c) 18x - 30
d) 16 - 12x
e) 6x + 12x²
f) 10x - 5x²
g) -2x² + 12x
3)
a) x² + 10x + 21
b) x² + 14x + 45
c) x² + 11x + 28
d) x² + 7x - 30
e) 2x² + 16x + 15
f) 6x² + 21x + 12
g) x² - 9
h) x² + 5x + 6 - (x² + 2x + 1) = 3x + 5
i) (x² + 4x - 12) - (x² - 2x - 3) = 6x - 9
Challenge: C Nm + (m+2)q
Page 2
1)
a) a + b = 3 + 7 = 10
b) 2a + 3b = 2(3) + 3(7) = 6 + 21 = 27
c) 3a + 2b + 5c = 3(3) + 2(7) + 5(4) = 9 + 14 + 20 = 43
d) 5a - 2b = 5(3) - 2(7) = 15 - 14 = 1
e) 3a + 2d = 3(3) + 2(-2) = 9 - 4 = 5
f) ab = 3 * 7 = 21
g) 2(a + b + c) = 2(3 + 7 + 4) = 2(14) = 28
h) a² + b² = 3² + 7² = 9 + 49 = 58
2)
a) (a + b)/c = (3 + 7)/(-4) = 10/(-4) = -2.5
b) (a - b + c)/(a + b) = (3 - 7 - 4)/(3 + 7) = (-8)/10 = -0.8
Factorise:
e) 6x - 18 = 6(x - 3)
f) 7x + 63 = 7(x + 9)
g) x² + 6x = x(x + 6)
h) 5x + 10x² = 5x(1 + 2x)
i) 16x² - 12x = 4x(4x - 3)
j) 14x - 21x² = 7x(2 - 3x)
3)
a) x² + 8x + 15 = (x + 3)(x + 5)
b) x² + 9x + 20 = (x + 4)(x + 5)
c) x² + 14x + 33 = (x + 3)(x + 11)
d) x² + 2x - 15 = (x + 5)(x - 3)
e) x² - 2x - 15 = (x - 5)(x + 3)
f) 3x² + 23x + 14 = (3x + 2)(x + 7)
g) 2x³ + 8x² + 8x = 2x(x² + 4x + 4) = 2x(x + 2)²
Page 3
1)
a) 3x = 36 → x = 12
b) x + 5 = 13 → x = 8
c) 15 = x + 4 → x = 11
d) 24 = 6x → x = 4
e) 2x + 3 = 15 → 2x = 12 → x = 6
f) x - 4 = 20 → x = 24
g) 4x = 32 → x = 8
h) 3x - 4 = 8 → 3x = 12 → x = 4
2)
a) 5x + 6 = 41 → 5x = 35 → x = 7
b) 6 + 2x = 18 → 2x = 12 → x = 6
c) 11 + 3x = 25 → 3x = 14 → x = 14/3
d) 4x + 15 = 12 → 4x = -3 → x = -3/4
e) 2x + 6 = x + 3 → x = -3
f) 4x - 8 = 5x - 2 → -x = 6 → x = -6
g) 6 - x = 5 → -x = -1 → x = 1
h) x + 4 = 10 - 2x → 3x = 6 → x = 2
3)
a) Perimeter = (x + 1) + (x + 2) + (x - 1) = 3x + 2
b) Perimeter = (x + 3) + (x + 1) + (x + 1) = 3x + 5
c) 3x + 2 = 14 → 3x = 12 → x = 4; Sides are 5cm, 6cm, 3cm.
d) 3x + 5 = 15 → 3x = 10 → x = 10/3; Sides are 19/3 cm, 13/3 cm, 13/3 cm.
Parent Tip: Review the logic above to help your child master the concept of algebraic manipulation worksheet.
