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NST Part IA EMB Pre-course quiz

The following exercises are intended to get you thinking about mathematics again before starting the EMB course. They are all based on the level of maths expected at Key Stage 4 Higher and GCSE. If you encounter any problems, please discuss these with your College supervisor.


(1) Approximations.

(i)        Round off the number 4384556 to 2 significant figures.

(ii)       Round off the number 4384556 to 3 significant figures.

(iii)      Round off the number 0.000033678 to 2 significant figures and write the result in scientific notation.

(iv)      Round off the number 3.14159265 to 3 decimal places.


(2) Fractions and percentages.

(i)        Evaluate   (1/2) + (1/3) .

(ii)       Evaluate    (1/2) × (1/3).

(iii)      Evaluate    (1/2) ÷ (1/3).

(iv)      Change     (3/20)  to a decimal.

(v)       Change     7 %      to a decimal.

(vi)      Change     (1/8)    to a percentage.

(vii)     What is the percent increase of a rise in temperature from 80° to 100°C?    

(Work this out for both the Kelvin and the Celsius temperature scales.)

 

(3) Order of operations.

Simplify the following expressions:

(i)        6 + 4 × 32.

(ii)       32 + 6(4 + 1).

(iii)      12 – 2(8 + 2) + 5.

(iv)      8[3(32 – 8) + 1].

(v)       6{4[2(3 + 2) – 8] – 8}.

(vi)      6(12 + 8) ÷ 2 + 1.

 

(4) Algebraic expressions.

(i)        Simplify the expression   x + 5 + 3x – 6 + 9x + 3 – 4.

(ii)       Simplify the expression   5y 2 – 4y + 8 – y 2 + 7y + 5.

(iii)      Multiply out the expression   (3x + 5) 2   and simplify the result.

(iv)      Simplify the expression   4(xy 3) 5.

(v)       Factorise the expression   8x 3 – 12x 2

(vi)      Factorise the expression   2x 2 – 8x + 6.

(vii)     Evaluate      if x = 2 and y = 6.


(5) Solving equations.

(i)        Solve the following equation for x:   5x + 7 = 2x + 13.

(ii)       Solve the following equation for y:   (4/7)y + 6 = 18.

(iii)      Solve the following equation for x:   x 2 – 6x + 8 = 0.

(iv)      Solve the following inequality for x:   4x – 3 < x – 6.

(v)       Solve the following equation for x:   x 2x – 4 = 0.

(vi)      Solve the following equation for x:   x 3 + 2x 2x – 2 = 0.

(vii)     Solve the following equation for a:   (a-1)/3 + (a+2)/6 = 2.


(6) Series.

(i)        The nth term in an arithmetic series of numbers, tn, can be expressed using the formula   

           tn = t1 + (n−1) d,   where t1 is the first term and d is the common difference between consecutive terms. Use this formula to determine the value of the 12th term in the following sequence: 3, 8, 13, 18, 23, … .

(ii)      The nth term in a geometric series of numbers, tn, can be expressed using the formula

          tn = t1 × r n1,    where t1 is the first term and r is the common ratio. If t1 = 1 and r = 3, evaluate the first six terms of the series.

(iii)      Work out a formula for the nth term of the following series: 32, 302, 3002, 30002, … .

 

(7) Coordinates and graphs.

For the points A and B, which have the (x, y) coordinates (1, 2) and (4, 6), respectively:

(i)       Determine the length of the line that connects A and B.

(ii)      Determine the slope of the line that connects A and B.

(iii)     Determine the equation of the straight line that goes through A and B, along with the coordinates of the points where this line intersects with the x and y axes.

(iv)     Determine the equation of the line parallel to AB that goes through the origin.

 

(8) Trigonometry and geometry.

(i)       Evaluate sin(30°), sin(120°), sin(210°), sin(300°) and .

(ii)      If a triangle has two angles equal to 110° and 20°, determine the size of the third angle.

(iii)     Let ABC be a triangle whose angles at A and B are 30° and 45°. If the side opposite angle B has length 9 cm, find the lengths of the remaining sides and the size of the angle at C.

(iv)     Calculate the surface area and the volume of a cube of side 4 cm.

 

Need some help?

There are many excellent web sites for revising mathematics at this level, including:

http://www.bbc.co.uk/schools/gcsebitesize/maths/