Quiz about HKDSE Maths MCQ Speed Training 4 (40 mins)

Question 1

[Ref.: HKDSE 2018 Q.31 (66%)]

Let f(x) be a quadratic function. The figure shown may represent the graph of y = f(x) and

Accepted Answer

C. the graph of y = - f(x + 6) .

Answer

A. the graph of y = - 3f(x) .

Answer

B. the graph of y = f(- 3x) .

Answer

D. the graph of y = f(- x + 15) .

Question 2

[Ref.: HKDSE 2019 Q.42 (65%)]

There are 4 white balls, 6 blue balls and 4 red balls in a bag. If 5 balls are randomly drawn from the bag at the same time, find the probability that at most 1 white ball is drawn.

Accepted Answer

B. $$\frac{6}{11}$$

Answer

A. $$\frac{5}{11}$$

Answer

C. $$\frac{81}{143}$$

Answer

D. $$\frac{7}{11}$$

Question 3

[Ref.: HKDSE 2012 Q.38 (63%)]

Which of the following may represent the graph of y = f(x) and the graph of y = f(x - 3) + 2 on the same rectangular coordinate system?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 4

[Ref.: HKDSE 2017 Q.43 (59%)]

When Andy throws a dart, the probability that he hits the target is 0.6. If Andy throws the dart 5 times, find the probability that he hits the target less than twice.

Accepted Answer

B. 0.087 04

Answer

A. 0.0256

Answer

C. 0.912 56

Answer

D. 0.9744

Question 5

[Ref.: HKDSE 2014 Q.44 (57%)]

In an examination, Andy gets 54 marks and his standard score is - 2 while Mary gets 70 marks and her standard score is 1.2. Find the mean of the examination scores.

Accepted Answer

C. 64 marks

Answer

A. 5 marks

Answer

B. 54 marks

Answer

D. 66 marks

Question 6

[Ref.: HKDSE 2019 Q.35 (53%)]

Consider the following system of inequalities:

Let D be the region which represents the solution of the above system of inequalities. If (x, y) is a point lying in D, then the greatest value of x + 2y + 2 is

Accepted Answer

D. 24.5 .

Answer

A. 14.5 .

Answer

B. 22 .

Answer

C. 23 .

Question 7

[Ref.: HKDSE 2015 Q.44 (52%)]

Bag P contains 1 white ball and 4 black balls while bag Q contains 3 white balls and 2 black balls. If a bag is randomly chosen and a ball is randomly drawn from the bag, find the probability that a white ball is drawn.

Accepted Answer

B. $$\frac{2}{5}$$

Answer

A. $$\frac{3}{10}$$

Answer

C. $$\frac{1}{2}$$

Answer

D. $$\frac{3}{5}$$

Question 8

[Ref.: HKDSE 2018 Q.42 (51%)]

There are 10 students from school A and 6 students from school B. If 4 students of the same school are selected to form a group, how many different groups can be formed?

Accepted Answer

C. 225

Answer

A. 15

Answer

B. 210

Answer

D. 1820

Question 9

[Ref.: HKDSE 2017 Q.38 (49%)]

In the figure, ABCD is a rectangle. If E is a point lying on AC such that AE = 26 cm, then DE =

Accepted Answer

A. $$\sqrt[]{601}$$ cm .

Answer

B. $$\sqrt[]{1105}$$ cm .

Answer

C. $$\sqrt[]{1825}$$ cm .

Answer

D. $$\sqrt[]{2329}$$ cm .

Question 10

[Ref.: HKDSE 2017 Q.45 (48%)]

Let m₁, r₁ and v₁ be the mean, the range and the variance of a group of numbers {x₁, x₂, x₃, x₄, x₅, x_6,x₇} respectively while m₂, r₂ and v₂ be the mean, the range and the variance of another group of numbers {3x₁ + 1, 3x₂ + 1, 3x₃ + 1, 3x₄ + 1, 3x₅ + 1, 3x₆ + 1, 3x₇+ 1} respectively. Which of the following must be true?

I. m₂ = 3m₁ + 1

II. r₂ = 3r₁ + 1

III. v₂ = 3v₁ + 1

Accepted Answer

A. I only

Answer

B. II only

Answer

C. I and III only

Answer

D. II and III only

Question 11

[Ref.: HKDSE 2016 Q.35 (47%)]

In the figure, SR is parallel to the y-axis. If (x, y) is a point lying in the shaded region PQRS (including the boundary), at which point does y - 2x + 1 attain its least value?

Accepted Answer

C. R

Answer

A. P

Answer

B. Q

Answer

D. S

Question 12

[Ref.: HKDSE 2019 Q.43 (47%)]

Polly needs to complete 3 tasks. The probabilities that she can complete each task on time are 0.4, 0.8 and 0.5 respectively. The probability that Polly can complete at most 2 tasks on time is

Accepted Answer

C. 0.84 .

Answer

A. 0.16 .

Answer

B. 0.68 .

Answer

D. 0.94 .

Question 13

[Ref.: HKDSE 2015 Q.36 (43%)]

In the figure, the equations of L₁, L₂ and L₃ are 4x + y - 8 = 0 , x + 2y + 4 = 0 and 2x - y + 8 = 0 respectively. If (h, k) is a point lying in the shaded region (including the boundary), which of the following must be true?

I. 4h + k > 8

II. h + 2k < - 4

III. 2h - k > - 8

Accepted Answer

B. III only

Answer

A. I only

Answer

C. I and II only

Answer

D. II and III only

Question 14

[Ref.: HKDSE 2017 Q.31 (42%)]

The figure shows the graph of $$y=f\left(x\right)$$ . If $$g\left(x\right)=f\left(\frac{x}{3}\right)$$ , which of the following may represent the graph of y = g(x)?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 15

[Ref.: HKDSE 2016 Q.34 (38%)]

Let u = $$\frac{8}{a+i}$$ and v = $$\frac{8}{a-i}$$ , where a is a real number. Which of the following must be true?

I. uv is a rational number.

II. The real part of u is equal to the real part of v .

III. The imaginary part of $$\frac{1}{u}$$ is equal to the imaginary part of $$\frac{1}{v}$$ .

Accepted Answer

B. II only

Answer

A. I only

Answer

C. I and III only

Answer

D. II and III only

Question 16

[Ref.: HKDSE 2013 Q.42 (37%)]

Find the range of values of k such that the circle x² + y² - 2x + 4y - 20 = 0 and the straight line 3x - 4y + k = 0 intersect at two distinct points.

Accepted Answer

A. - 36 < k < 14

Answer

B. - 14 < k < 36

Answer

C. k < - 36 or k > 14

Answer

D. k < - 14 or k > 36

Question 17

[Ref.: HKDSE 2016 Q.39 (35%)]

In the figure, ABCDEFGH is a rectangular block. AC and BD intersect at P . Q is a point lying on CH such that CQ = 16 cm and QH = 56 cm. Find $$\sin\angle PFQ$$ .

Accepted Answer

C. $$\frac{440}{13\sqrt[]{6736}}$$

Answer

A. $$\frac{34}{\sqrt[]{6736}}$$

Answer

B. $$\frac{78}{\sqrt[]{6736}}$$

Answer

D. $$\frac{972}{13\sqrt[]{6736}}$$

Question 18

[Ref.: HKDSE 2019 Q.32 (35%)]

If $$\frac{5}{\log x\ -\ 2}-4=\frac{6}{\log x+3}$$ , then $$\log\frac{1}{x}$$ =

Accepted Answer

B. - 3 or $$\frac{17}{4}$$ .

Answer

A. 3 or $$-\frac{17}{4}$$ .

Answer

C. $$\frac{1}{3}$$ or $$-\frac{4}{17}$$ .

Answer

D. $$-\frac{1}{3}$$ or $$\frac{4}{17}$$ .

Question 19

[Ref.: HKDSE 2018 Q.32 (34%)]

The figure shows the graph of y = log_a x and the graph of y = log_b x on the same rectangular coordinate system, where a and b are positive constants. If a vertical line cuts the graph of y = log_a x, the graph of y = log_b x and the x-axis at the points A, B and C respectively, which of the following is/are true?

I. b > 1

II. a > b

III. $$\frac{AB}{BC}=\log_ab$$

Accepted Answer

A. I only

Answer

B. II only

Answer

C. I and III only

Answer

D. II and III only

Question 20

[Ref.: HKDSE 2019 Q.31 (34%)]

In the figure, the straight line L shows the relation between log₉ x and log₉ y. It is given that L passes through the points (6, 4) and (18, 7). If y = kx^a, then k =

Accepted Answer

D. 243 .

Answer

A. $$\frac{1}{4}$$ .

Answer

B. $$\sqrt[]{3}$$ .

Answer

C. $$\frac{5}{2}$$ .

Question 21

[Ref.: HKDSE 2014 Q.40 (33%)]

In the figure, AB is a vertical pole standing on the horizontal ground BCD, where $$\angle CBD=90\degree$$ . If the angle between the plane ACD and the horizontal ground is $$ heta$$ , then $$ an heta$$ =

Accepted Answer

D. $$\frac{25}{24}$$ .

Answer

A. $$\frac{7}{24}$$ .

Answer

B. $$\frac{24}{7}$$ .

Answer

C. $$\frac{24}{25}$$ .

Question 22

[Ref.: HKDSE 2019 Q.37 (31%)]

If the straight line x + 2y = k and the circle x² + y² + 4x + 2y - 1 = 0 intersect at two distinct points A and B, then x-coordinate of the mid-point of AB is

Accepted Answer

C. $$\frac{k-6}{5}$$ .

Answer

A. k - 6 .

Answer

B. k + 6 .

Answer

D. $$\frac{k+6}{5}$$ .

Question 23

[Ref.: HKDSE 2015 Q.42 (30%)]

The coordinates of the points P, Q and R are (1, 0), (7, 9) and (-2, 9) respectively. Find the y-coordinate of the orthocentre of $$\Delta PQR$$ .

Accepted Answer

C. 7

Answer

A. 3

Answer

B. 5

Answer

D. 9

Question 24

[Ref.: HKDSE 2012 Q.40 (30%)]

The base of a solid right pyramid is a square of side 6 cm. If the height of the pyramid is 4 cm, find the angle between the plane VDC and the plane VBC correct to the nearest degree.

Accepted Answer

D. 111o

Answer

A. 53o

Answer

B. 56o

Answer

C. 90o

Question 25

[Ref.: HKDSE 20198 Q.39 (28%)]

In the figure, EC is a tangent to the circle ABCD at the point C . AE is a straight line which cuts the circle ABCD at D. If AB // EC, arc AD = arc CD and $$\angle EAB=102\degree$$ , then $$\angle BCE$$ =

Accepted Answer

C. 112o .

Answer

A. 104o .

Answer

B. 108o .

Answer

D. 116o .

Question 26

[Ref.: HKDSE 2018 Q.43 (26%)]

There are 8 number cards each with a number 1, 2, 3, 4, 5, 6, 7 and 8 respectively. Matthew and Richard take turns to draw a card with replacement until one of them gets a '2' or '4'. Matthew draws a card first. Find the probability that Matthew gets a number '4'.

Accepted Answer

B. $$\frac{2}{7}$$ .

Answer

A. $$\frac{1}{7}$$ .

Answer

C. $$\frac{3}{7}$$ .

Answer

D. $$\frac{1}{2}$$ .

Question 27

[Ref.: HKDSE 2015 Q.45 (26%)]

Let x₁, y₁ and z₁ be the mean, the median and the variance of a group of numbers {a₁, a₂, a₃, ..., a₁₀₀} respectively while x₂, y₂ and z₂ be the mean, the median and the variance of the group of numbers {a₁, a₂, a₃, ..., a₉₉} respectively. If x₁ = a₁₀₀, which of the following must be true?

I. x₁ = x₂

II. y₁> y₂

III. z₁ < z₂

Accepted Answer

B. I and III only

Answer

A. I and II only

Answer

C. II and III only

Answer

D. I, II and III

Question 28

[Ref.: HKDSE 2018 Q.40 (20%)]

It is given that k is a negative constant. The straight line 3x + 4y = k cuts the x-axis and the y-axis at the points P and Q respectively. Let R be a point lying on the y-axis such that the x-coordinate of the orthocentre of $$\Delta PQR$$ is 3 . Find the y-coordinate of R .

Accepted Answer

B. - 4

Answer

A. - 25

Answer

C. 4

Answer

D. 25

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