National 5 Revision

Surds and Indices

100

Simplify √128

8√2

200

a⁰(a³xa⁴)

a⁷

300

2√2 + 4√18

14√2

400

Rationalise the denominator of:

1/(

√

500

(y^1/2 x y^3/2)/(y^2/3 x y^1/3)

y

Vectors and Lines

100

If the vector u has components (2 5 6), what is |u|?

√65

200

Find the gradient of a line with the points (4,5) and (3,7)

m=-2

300

What is the gradient of the line with the formula:

4x + 3y - 2 = 0

m = -4/3

400

Find the gradient and y-intercept of 

4y + 2x - 3 = 0

m = -1/2

Y-Int = (0, 3/4)

500

I travel along vector v = (2 8 1), then in the opposite direction of vector p = (3 9 4) and finally along vector y = (3 5 7). What is the resultant vector r's magnitude?

r = (2 4 4)

|r| = 6

Statistics

100

Find the mean of the following data:

26 54 34 12 23 4

25.5

200

Find the mode, median and range of the data:

2 7 8 8 10 14 16 21

Mode = 8

Median = 9

Range =19

300

List the 3 quartiles of the data:

10 13 14 16 19 24 27

Q₁=13

Q₂=16

Q₃=24

400

Find the Semi-Interquartile Range of the following data:

2 7 8 8 10 14 16 21

7.5

500

Find the standard deviation of the data set:

2 5 6 8 9

2.74

Trigonometry

100

What does sin²x + cos²x equal?

1

200

Simplify tanxcosx

sinx

300

Solve the equation:

2sinx=1

0 < x < 360

x=30⁰, x=150⁰

400

Simplify

sin³x + sinxcos²x

sinx

500

Solve the equation:

7 + 5cosx = 9

0 < x < 360

x = 66.42, x = 293.58

Algebra and Quadratics

100

Factorise 

x² + 6x - 16

(x + 8)(x - 2)

200

Change the subject of the formula to p: 

p² + q² = r²

p=√(r²-q²)

300

Complete the square for

x²+10x-14

(x+5)²-39

400

Change the subject of the formula to b:

a² = 2ab² + d

b = √((a² - d)/2a)

500

What are the roots and what is the turning point of:

x² - 10x + 25

x = 5

(5,0)