Daily Practice · Higher Plus
April 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 1999 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1999Simplify sqrt(32) + sqrt(2), giving your answer in the form a sqrt(b).
- 2nd April 1999Make x the subject of 5x + 3 = y(x + 3).
- 3rd April 1999y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 4th April 1999A cuboid measures 14 cm by 13 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th April 1999A 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?
- 6th April 1999On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th April 1999A rectangle is 11 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th April 1999Write 2/(x + 2) + 5/(x - 5) as a single fraction.
- 9th April 1999y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 10th April 1999A cuboid measures 11 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th April 1999A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th April 1999A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 13th April 1999Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 14th April 1999Solve 20x^2 + 29x + 5 = 0.
- 15th April 1999y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 81.
- 16th April 1999The 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.
- 17th April 1999A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 18th April 1999On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th April 1999A block has mass 620 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th April 1999f(x) = 6x + 8. Work out the inverse function f^-1(x).
- 21st April 1999A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd April 1999In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 23rd April 1999The probability of winning a game is 3/4. A player expects 27 wins. How many games did they play?
- 24th April 1999A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 25th April 1999x = 200 and y = 52, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th April 1999Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 27th April 1999y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 28th April 1999In a vector proof you find that vector PQ = a + 6b and vector RS = 3a + 18b. What does this show about PQ and RS?
- 29th April 1999A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 30th April 1999On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?