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IB Mathematics AA SL - Revision Ladder

Level 1

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Paper 2

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Question 1

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easy

[Maximum mark: 6]

Consider an arithmetic sequence 2,6,10,14,2,6,10,14,\dots

  1. Find the common difference, dd. [2]

  2. Find the 1010th term in the sequence. [2]

  3. Find the sum of the first 1010 terms in the sequence. [2]

easy

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Question 2

no calculator

easy

[Maximum mark: 5]

The following box-and-whisker plot represents the commute time, in minutes, for a group of workers.

9e28a9e7a6be31076ba32a58199c00ff7ac4e0ab.svg

  1. Write down the median commute time. [1]

The range is 2323 minutes, and the interquartile range is 1010 minutes.

  1. Find the value of:
    1. pp;

    2. qq. [4]

easy

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Question 3

no calculator

easy

[Maximum mark: 7]

Let f(x)=(x3)(x+1)f(x) = (x - 3)(x + 1), for xRx \in \mathbb{R}.

For the graph of ff, find:

  1. the yy-intercept; [2]

  2. the xx-intercepts; [2]

  3. the coordinates of the vertex. [3]

easy

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Question 4

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easy

[Maximum mark: 6]

Find the value of each of the following, giving your answer as an integer.

  1. log66\log_6 6. [2]

  2. log69+log64\log_6 9 + \log_6 4. [2]

  3. log672log62\log_6 72 - \log_6 2. [2]

easy

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Question 5

calculator

easy

[Maximum mark: 5]

In a triangle ABC, AB=6\text{AB} = 6 cm, BC=10\text{BC} = 10 cm and CBˆA=70°\text{C\^{B}A} = \ang{70}.

  1. Find the area of the triangle. [2]

  2. Find AC\text{AC}. [3]

Give your answers correct to 33 significant figures.

easy

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Question 6

no calculator

easy

[Maximum mark: 5]

Note: In this question, distance is in metres and time is in seconds.

A tennis ball is thrown in the air. Its height hh above the ground after time tt is given by

h(t)=5t2+20t+4, for 0t4.\begin{aligned} \\ h(t) = -5t^2+20t+4, \textrm { for } 0 \leq t \leq 4.\end{aligned}
  1. Find h(t)h'(t). [2]

  2. Find the maximum height attained by the ball. [3]

easy

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Question 7

no calculator

easy

[Maximum mark: 7]

The following Venn diagram shows two events AA and BB, where P(A)=0.3\mathrm{P}(A) = 0.3, P(AB)=0.2\mathrm{P}(A\cap B) = 0.2 and P(AB)=0.7\mathrm{P}(A\cup B) = 0.7. The values of pp, qq, rr and ss are probabilities\text{probabilities}.

8ca7dc69310d14eee80cfb8fc216080fc079bcf5.svg

  1. Write down the value of rr. [1]

  2. Find the value of:

    1. pp;

    2. qq;

    3. ss. [4]

  3. Find P(B)\mathrm{P}(B). [2]

easy

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Question 8

no calculator

easy

[Maximum mark: 5]

Let f(x)=x2+2x+3f(x) = -x^2+2x+3. The graph of ff is shown in the following diagram.

9b151d369be7a9d5947f25e37a1d88fcf6e38455.svg

  1. Find (x2+2x+3)dx\displaystyle \int (-x^2+2x+3) \,\mathrm{d}x. [2]

  2. Find the area of the shaded region. [3]

easy

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Question 9

calculator

easy

[Maximum mark: 6]

A coffee shop owner believes that the number of coffees they sell on a given day is related to the average temperature of that day. The average temperature TT, in degrees Celsius, on seven randomly selected days is shown in the following table. The table also shows the number of coffees, NN, the coffee shop sells on those seven days.

e182b3471e48ce381f17d81a5fd34ed73e64dd78.svg

  1. The relationship between the variables can be modelled by the regression equation N=aT+bN = aT+b.

    1. Find the value of aa and the value of bb.

    2. To the nearest integer, estimate the number of coffees sold on a day when the average temperature is 1616 °C\text{\textdegree{C}}. [4]

  2. Find the value of rr, the correlation coefficient. [2]

easy

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Question 10

no calculator

easy

[Maximum mark: 4]

Expand (2x+1)4(2x + 1)^4 in descending powers of xx and simplify your answer.

easy

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