IAL P2 revision

Multiple Select

Which among the following is true?

• Trapezium rule will give an estimate or approximate area under a curve.

• Trapezium rule is used to get an exact area under a curve

Multiple Select

In the trapezium rule below, h =?

$$\int_a^bf\left(x\right)dx=\frac{1}{2}h\left[y_o+2\left\{y_1+y_2+..y_{n-1}\right\}+y_n\right]$$  

• $$h=\frac{b+a}{n}$$

• $$h=\frac{b+a}{n+1}$$  

• $$h=\frac{b-a}{n}$$

• $$h=\frac{b-a}{n+1}$$

Multiple Choice

A table of values MUST be drawn when applying the Trapezium Rule.

• True

• False

​Trapezium Rule

• If there are n strips, n+1 points will be used

• We must use ALL the values of y from the table

• h (height) in the formula is the STEP between the values of x

• Use RADIAN when there are trigonometric functions

• The formula is GIVEN on the formulae booklet

Multiple Choice

$$\int_1^2\left(2x+k\right)dx=8.$$   $$\ k=?$$  

• $$4$$  

• $$5$$  

• $$-3$$  

• $$-2$$  

Multiple Choice

If $$\int_0^2f\left(x\right)\ dx=5$$ ,  $$\int_2^4f\left(x\right)dx=3$$  , and  $$\int_2^6\ f\left(x\right)dx\ =12$$  , then  $$\int_0^6\ f\left(x\right)\ dx=$$  

• 5

• -5

• 17

• 20

Multiple Choice

The area of the region enclosed by the curves can be found by

• $$\int_0^42x^{\frac{1}{2}}-\frac{1}{4}x^2dx$$

• $$\int_0^42x^{\frac{1}{2}}+\frac{1}{4}x^2dx$$

• $$\int_0^4\ \frac{1}{4}x^2-2x^{\frac{1}{2}}dx$$

Multiple Choice

The area of the region enclosed by the curves can be found by

• $$\int_{-1}^0-2x^2-4x-4+\frac{x}{2}+3\ dx$$

• $$\int_{-1}^0\ \frac{x}{2}+3+2x^2+4x+4\ dx$$

• $$\int_{-1}^0\ -2x^2-4x-4-\frac{x}{2}-3\ dx$$

​Definite integral & Area between curves

Differentiation

• questions finding stationary point(s)

• questions finding increasing or decreasing interval(s)

• graph sketching

• chain rule, product rule, quotient rule and differentiating implicit functions are NOT expected in P2

Multiple Choice

Fully simplify $$\log_612+\log_615-\log_65$$ .

• $$\log_622$$

• 22

• 2

• -2

Multiple Choice

Expand: $$\log\ ab$$  

• $$\log a\ -\ \log b$$  

• $$b\log a$$  

• $$a\log b$$  

• $$\log a+\log b$$  

Multiple Choice

Which of the logarithms below is equivalent to the following: $$2\log12$$  

• $$\log14$$

• $$\left(\log12\right)^2$$

• $$\log24$$

• $$\log144$$

Math Response

If $$\log_2\ x=a$$ , then $$\log_2\left(16x\right)=?$$

Type answer here

Correct Answer: 4+a

Deg^°

Rad

Math Response

If $$\log_2\ x=a$$ , then $$\log_2\left(\frac{x^4}{2}\right)=?$$

Type answer here

Correct Answer: 4a-1

Deg^°

Rad

​Law of logarithms

Law of logarithms

On formulae booklet

​Worth noted

Multiple Select

Solve $$3^x=5$$

• $$x=\log5-\log3$$

• $$x=\log\left(\frac{5}{3}\right)$$

• $$x=\log_35$$

• $$x=\frac{\log5}{\log3}$$

Multiple Choice

Solve $$\log_5x=2$$

• 10

• 25

• $$\log25$$

• $$\log5+\log2$$

Multiple Choice

The equation $$2\log_3\left(x-5\right)-\log_3\left(2x-13\right)=2$$ can be written as

• $$2\left(x-5\right)-\left(2x-13\right)=6$$

• $$2\left(x-5\right)-\left(2x-13\right)=9$$

• $$\left(x-5\right)^2=9\left(2x-13\right)$$

• $$\left(x-5\right)^2=6\left(2x-13\right)$$

​Log/exp equations

Multiple Choice

In the equation (x-3)²+(y+2)²=10, the center of the circle is...

• (3, 2)

• (3, -2)

• (-3, 2)

• (-3, -2)

Multiple Choice

In the equation (x-3)²+(y+2)²=10, the radius of the circle is...

• 10

• 5

• 1

• $$\sqrt[]{10}$$

Multiple Choice

What is the equation of this circle?

• (x + 3)² + (y - 1)² = 9

• (x - 3)² + (y + 1)² = 9

• (x - 3)² + (y + 1)² = 3

• (x + 3)² + (y - 1)² = 3

Multiple Choice

The SLOPE of the tangent to the circle x²+y²=25 at the point (3, 4) is...

• $$\frac{3}{4}$$

• $$\frac{4}{3}$$

• $$-\frac{3}{4}$$

• $$-\frac{4}{3}$$

​Circles

• perpendicular bisector of chord passes through centre

• tangent perpendicular to radius

• angles in semi-circle

• "Finding the slope of tangent by differentiation" is NOT expected in questions of circles

Multiple Choice

Find the remainder when the polynomial

x⁴ + x³ - 2x² + 3x + 7 is divided by (x+1).

• R=14

• R=10

• R=2

• R=4

Multiple Choice

If dividing polynomial g(x) by (x – 1) yields a remainder of 2, which must be true?

• g(1) = 2

• g(-1) = 2

• g(2) = 1

• g(2) = -1

Multiple Choice

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9

• $$3x^2-3x+8-\frac{9}{x+1}$$

• $$3x^2+3x+8+\frac{7}{x+1}$$

• 3x³ + 3x² + 8x + 7

​Remainder/Factor theorem

Multiple Choice

What is the formula for the sum of the first n terms of a geometric sequence?

• $$ar^n$$

• $$ar^{n-1}$$

• $$\frac{a\left(1-r^n\right)}{1-r}$$

• None of these

Multiple Choice

$$-3,\ \ 6,\ -12,\ \ 24,\ ....$$  Find the common ratio

• 3

• -2

• 2

• $$\frac{1}{2}$$  

Multiple Choice

Write down the first four terms of the sequence if u₁ = 1 and u_n+1 = 2u_n + 4.

• 0, 4, 12, 28

• 1, 4, 10, 18

• 1, 4, 12, 28

• 1, 6, 16, 36

• 6, 16, 34, 72

Multiple Select

Which of the following geometric sequences have FINITE sum to infinity?

• 1, 2, 4, 8, 16, ...

• 16, 8, 4, 2, 1, ...

• -3, 9, -27, 81, ...

• -81, 27, -9, 3, -1, ...

Sequence

• A.P. common difference,  u_n + u_n+2 = 2 x u_n+1

• G.P. common ratio, u_n x u_n+2 = (u_n+1)²

• u_n-1, the previous term

• u_n, the term being considered

• u_n+1, the next term

• u_n+2, the next term of the next term

• sigma notation is expected

Binomial theorem

• Different types of notations,
  
  

  
  are expected

​Trigonometry

• Be careful of using radians or degrees

• Compound angle formulae and
  related identities are NOT expected

• The Symmetry of sin, cos, tan solution

​Proof by exhaustion

• for finite range, e.g. 1 ≤ x ≤ 5, show all possible cases

• for "all natural numbers", use grouping
  two groups : 2k, 2k+1
  three groups : 3k, 3k+1, 3k+2
  or other grouping if necessary

You should

memorise

Formulae

booklet

provides

Formulae

booklet

provides