Daily Practice · Higher Plus
August 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2003A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 2nd August 2003A car covers 230 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.
- 3rd August 2003f(x) = 5x - 4 and g(x) = 3x + 4. Work out fg(1).
- 4th August 2003y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 5th August 2003In a vector proof you find that vector PQ = 2a + 3b and vector RS = 10a + 15b. What does this show about PQ and RS?
- 6th August 2003A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 7th August 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?
- 8th August 2003Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 9th August 2003The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 10th August 2003y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 11th August 2003A cuboid measures 3 cm by 12 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th August 2003A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th August 2003A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 14th August 2003Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 15th August 2003A quadratic sequence starts 0, -1, 0, 3. Work out the second difference, and the coefficient of n^2.
- 16th August 2003y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 9.
- 17th August 2003A cuboid measures 13 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th August 2003A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th August 2003On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th August 2003A rectangle is 16 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st August 2003Solve x^2 + 9x + 8 < 0.
- 22nd August 2003A train slows steadily from 28 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd August 2003The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 24th August 2003A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 25th August 2003A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 26th August 2003Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 27th August 2003Write x^2 - 14x + 11 in the form (x + a)^2 + b.
- 28th August 2003y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 29th August 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.
- 30th August 2003The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 31st August 2003On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?