Daily Practice · Higher Plus
July 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2004 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2004A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 2nd July 2004A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 3rd July 2004A car covers 330 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th July 2004Work out the coordinates of the turning point of y = x^2 + 14x - 1.
- 5th July 2004y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 6th July 2004A cuboid measures 15 cm by 13 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th July 2004A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th July 2004On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th July 2004Rationalise the denominator of 10/sqrt(5), giving your answer in its simplest form.
- 10th July 2004Simplify (x^2 + x - 6)/(x - 2).
- 11th July 2004y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 12th July 2004A cuboid measures 11 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th July 2004A bag holds 6 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th July 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?
- 15th July 2004Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
- 16th July 2004In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 17th July 2004y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 25.
- 18th July 2004The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 19th July 2004A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 20th July 2004On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st July 2004A rectangle is 22 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd July 2004Make x the subject of 8x + 8 = y(x + 8).
- 23rd July 2004A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 24th July 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.
- 25th July 2004The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?
- 26th July 2004A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 27th July 2004Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 28th July 2004Write 6/(x + 3) + 7/(x - 1) as a single fraction.
- 29th July 2004y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 30th July 2004In a vector proof you find that vector PQ = 4a + b and vector RS = 12a + 3b. What does this show about PQ and RS?
- 31st July 2004A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.