Daily Practice · Higher Plus
April 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2004 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2004In a vector proof you find that vector PQ = 4a - b and vector RS = 8a - 2b. What does this show about PQ and RS?
- 2nd April 2004A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 3rd April 2004On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th April 2004x = 174 and y = 122, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th April 2004In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 6th April 2004y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 7th April 2004A cuboid measures 14 cm by 11 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th April 2004A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th April 2004A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 10th April 2004A car covers 720 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th April 2004Make x the subject of 7x + 8 = y(x + 8).
- 12th April 2004y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 81.
- 13th April 2004A cuboid measures 14 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th April 2004A bag holds 7 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th April 2004On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th April 2004Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 17th April 2004Write 2/(x + 2) + 6/(x - 6) as a single fraction.
- 18th April 2004A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
- 19th April 2004The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 20th April 2004A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 21st April 2004A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 22nd April 2004Simplify sqrt(48) + sqrt(147), giving your answer in the form a sqrt(b).
- 23rd April 2004Solve 20x^2 + 7x - 3 = 0.
- 24th April 2004y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 25th April 2004In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 26th April 2004The probability of winning a game is 1/2. A player expects 22 wins. How many games did they play?
- 27th April 2004On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th April 2004A rectangle is 13 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th April 2004f(x) = 8x - 2. Work out the inverse function f^-1(x).
- 30th April 2004y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.