Year 10 2020 5 3 at3

bài kiểm tra lớp 10, equation, quadratic equation, simultaneous equation, bivariate data analysis, bài kiểm tra toán tiếng anh đại số lớp 10

Section I Simultaneous Equations (9 marks)

1 Use the graph to determine the solution for the following pair of simultaneous equations:

y = 4 – 2x y = 3x – 1

x-4-224

y

-4-224 y = 3x – 1

2

3 Solve the equations and simultaneously, showing all working out 3

4 Two positive integers differ by 3 and the sum of their squares is 117 Find the numbers by forming equations and solving simultaneously 3

Section II Bivariate Data (20 marks)

1 Rick and George have played 20 rounds of golf on their local golf course The scores are recorded, and the mean and standard deviation are recorded in the table below:

Person Mean Standard Deviation Rick 80 5.6 George 80 9.2 Based on these results, in their next game, who is most likely to have: (a) The lower score Give a reason for your answer 2 (b) The higher score Give a reason for your answer 2 2 For a class of 8 students, the percentage Maths and English were: as follows:

Maths: 72, 63, 87, 94, 55, 46, 66, 81 English: 61, 39, 52, 45, 79, 59, 51, 63 (a) Using your calculator calculate the mean and Standard Deviation for the maths and English

results above: Subject Mean Standard Deviation Maths

English

2

(b) Tom scored 75 in Maths and 70 in English, which is the better mark, relative to the class

5 Choose a word to describe the strength and relationship of the following diagrams

NO RELATIONSHIP, WEAK NEGATIVE, STRONG NEGATIVE, WEAK POSITIVE STRONG POSITIVE

3

6 The heights and shoe size of a group of year 11 were measured and recorded below:

Height (cm) 174 177 180 179 176 170 175 173 180 178 Shoe Size 10 10 11 11 9.5 7.5 9 11.5 12.5 11

Height (cm) 183 178 173 179 174 175 Shoe Size 12.5 12 9.5 10.5 9 10.5

The graph of the scatter plot is shown below

(a) Identify the dependent variable 1 (b) Identify the independent variable 1 (c) Use the graph the extrapolate the shoe size of a student with a height of 185 cm 1 (d) Determine the equation of the line of best fit by using the points (170, 7.5) and (180, 12)

as two points the straight line passes through 2

7 A survey was conducted on each day of the weekend to determine the ages of children using treetops adventure centre Twenty children were surveyed each day The results of the survey are recorded in the box plots

(a) How many children were at least 9 years old on Sunday? 2

(b) Compare and contrast the two sets of results by referring to the distribution and the measures of location and spread 2

Section III Quadratic Equations (24 marks)

1 Solve the following equations a) (2𝑥𝑥 + 1)(𝑥𝑥 − 1) = 0 1

b) 𝑥𝑥2 − 3𝑥𝑥 = 0 1

c) 𝑥𝑥2 − 3𝑥𝑥 + 2 = 0 2

e) 5𝑥𝑥2 + 3𝑥𝑥 − 2 = 0 2

f) 10𝑥𝑥2 − 𝑥𝑥 − 21 = 0 2

g) 1𝑥𝑥 −

1

h) (3𝑥𝑥 + 4)(𝑥𝑥 − 3) = 16 2

2 Solve the following by completing the square, leave answer in simplest surd form (if applicable)

2𝑥𝑥2 = −7𝑥𝑥 + 30 3

3 Solve the following by using the quadratic formula Leave your answer in simplest surd form, showing all working 2

3𝑥𝑥2− 15 = 0

4 a) Solve 𝑥𝑥2+ 8𝑥𝑥 + 20 = 0, showing all working out 1

b) Explain your answer 1

5 Solve ( 2𝑥𝑥)2− 12(2𝑥𝑥) + 32 = 0 2

6 Find the point(s) of intersection of the line 𝑦𝑦 = 𝑥𝑥 and the parabola 𝑦𝑦 = 𝑥𝑥(𝑥𝑥 − 1) algebraically (Show all working) 3