Daily Practice · Higher Plus
April 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2003 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2003In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 2nd April 2003The probability of winning a game is 1/2. A player expects 10 wins. How many games did they play?
- 3rd April 2003A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 4th April 2003Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 5th April 2003Work out the nth term of the quadratic sequence 13, 28, 51, 82, ...
- 6th April 2003y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 7th April 2003In a vector proof you find that vector PQ = a + 5b and vector RS = 3a + 15b. What does this show about PQ and RS?
- 8th April 2003A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 9th April 2003On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th April 2003Simplify sqrt(8) + sqrt(50), giving your answer in the form a sqrt(b).
- 11th April 2003The point (-3, -5) lies on y = f(x). Write down its image on y = f(x + 4).
- 12th April 2003y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 13th April 2003A cuboid measures 14 cm by 10 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th April 2003A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th April 2003A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 16th April 2003A rectangle is 18 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th April 2003Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 18th April 2003y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 16.
- 19th April 2003A cuboid measures 11 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th April 2003A bag holds 3 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st April 2003On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd April 2003Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 23rd April 2003f(x) = 6x - 6 and g(x) = 5x - 3. Work out fg(6).
- 24th April 2003A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 25th April 2003The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 26th April 2003A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 27th April 2003A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 28th April 2003A block has mass 650 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th April 2003The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 30th April 2003y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.