Y10 Quadratics Ext Lesson 1 (5.3 Advance) - Homework

Y10 Quadratics – Lesson 1
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Lesson 1 Homework:
9.
Solve the equation
𝑥−𝑎
𝑥+𝑎
=
𝑥+𝑎
2𝑥−𝑎
for x, where a is
a constant.
Developmental Questions
2.
Solve the following by factorising and using
a)
b)
c)
d)
e)
f)
the quadratic formula
a)
b)
c)
d)
e)
f)
−3𝑥 2 + 2𝑥 + 1
𝑥 2 − 2𝑥 + 1 = 0
5𝑥 2 − 3𝑥 − 2 = 0
𝑥 2 − 5𝑥 + 1
−2𝑥 2 + 4𝑥 + 6 = 0
−8𝑥 2 − 4𝑥 + 10 = 0
−3𝑥 2 + 2𝑥 + 1
𝑥 2 − 2𝑥 + 1 = 0
5𝑥 2 − 3𝑥 − 2 = 0
𝑥 2 − 5𝑥 + 1
−2𝑥 2 + 4𝑥 + 6 = 0
−8𝑥 2 − 4𝑥 + 10 = 0
11. Solve the following equations
Exam Style Questions
2.
10. Solve the following by completing the square
The golden ratio is defined as the positive
1
number that satisfies 𝑎 =
. What is the
1+𝑎
value of 𝑎?
a) 𝑥 4 − 𝑥 2 − 6 = 0
b) (3𝑥 )2 − 2(3𝑥 ) − 3 = 0
c) 5(2𝑥 )2 + 14(5𝑥 ) − 3 = 0
12. Solve the following:
(a) 6𝑥 6 − 7𝑥 3 + 2 = 0
1 2
2
3.
One of the solutions of the equation 2𝑥 +
𝑏𝑥 − 1 = 0 is 𝑥 = 1. Find the other solution.
4.
Solve
13. Solve 𝑥 2 − 4𝑥 − 2 = 0 by completing the
square.
3
𝑥
8
+
=
.
𝑥 − 2 𝑥 + 2 𝑥2 − 4
5.
Solve 𝑥 + 4√𝑥 = 60
6.
Solve = 𝑥 − 1 leaving your answer in exact
𝑥
form.
7.
MCQ: The 𝑥-coordinates of the points 𝐴 and
𝐵 are
4
a)
b)
c)
d)
8.
𝑥
𝑥
𝑥
𝑥
1
(b) (𝑥 + ) − 2 (𝑥 + ) − 8 = 0
𝑥
𝑥
(c) 9𝑥 + 7(3𝑥 ) + 6 = 0 by letting 𝑦 = 3𝑥 .
3
= − ,𝑥 = 1
2
= 2, 𝑥 = −3
3
= −1, 𝑥 =
2
= −2, 𝑥 = 3
Solve √8 − 7𝑥 = 𝑥.
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Y10 Quadratics – Lesson 1
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Answers
Developmental Questions
1.
1
(a) 𝑥 = − , 1
3
(b) 𝑥 = 1
2
(c) 𝑥 = − , 1
5
5±√21
(d) 𝑥 =
2
(e) 𝑥 = −1,3
(f) 𝑥 =
−1±√21
4
Exam Style Questions
−1±√5
2.
𝑎=
3.
4.
5.
𝑥 = − ,1
2
𝑥 = −2, 1
𝑥 = 36, 100
6.
7.
8.
9.
10.
𝑥=
2
C
𝑥 = −8, 1
𝑥 = 0, 5𝑎
2
1
1±√17
1
(a) 𝑥 = − , 1
3
(b) 𝑥 = 1
2
(c) 𝑥 = − , 1
5
5±√21
(d) 𝑥 =
2
(e) 𝑥 = −1,3
(f) 𝑥 =
−1±√21
4
11.
(a) 𝑥 = ±√3
(b) 𝑥 = 1
(c) 𝑥 = −2.32
12.
3 2
1
(a) 𝑥 = √ , 3
3
√2
(b) 𝑥 = 2 ± √3, −1
(c) 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
13. 𝑥 = 2 ± √6
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