Daily Practice · Higher Plus
July 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2003The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 2nd July 2003On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd July 2003Simplify sqrt(75) + sqrt(3), giving your answer in the form a sqrt(b).
- 4th July 2003Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 5th July 2003A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
- 6th July 2003In a vector proof you find that vector PQ = 2a - b and vector RS = 8a - 4b. What does this show about PQ and RS?
- 7th July 2003A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 8th July 2003A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 9th July 2003A rectangle is 8 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th July 2003Use the iteration x(n+1) = cube root of (5x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 11th July 2003y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 12th July 2003A cuboid measures 7 cm by 7 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th July 2003A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th July 2003On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th July 2003Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 16th July 2003Work out the nth term of the quadratic sequence -1, 1, 5, 11, ...
- 17th July 2003y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 18th July 2003A cuboid measures 4 cm by 8 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th July 2003A bag holds 4 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th July 2003A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 21st July 2003A block has mass 450 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd July 2003The point (-6, 5) lies on y = f(x). Write down its image on y = f(x + 1).
- 23rd July 2003y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 81.
- 24th July 2003The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 25th July 2003A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 26th July 2003On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th July 2003x = 200 and y = 100, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th July 2003Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 29th July 2003A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 30th July 2003In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 31st July 2003The probability of winning a game is 2/5. A player expects 26 wins. How many games did they play?