Daily Practice · Higher Plus
March 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in March 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' March 1999 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1999On 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?
- 2nd March 1999Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 3rd March 1999Solve x^2 - 12x + 27 < 0.
- 4th March 1999A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 5th March 1999A cuboid measures 4 cm by 5 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th March 1999A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th March 1999A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 8th March 1999A block has mass 660 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th March 1999Write x^2 - 14x + 9 in the form (x + a)^2 + b.
- 10th March 1999y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 11th March 1999A cuboid measures 7 cm by 4 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th March 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?
- 13th March 1999On 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?
- 14th March 1999x = 176 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th March 1999Work out the coordinates of the turning point of y = x^2 - 10x + 5.
- 16th March 1999y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 17th March 1999The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 18th March 1999A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 19th March 1999A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 20th March 1999A car covers 870 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st March 1999Simplify (x^2 - 4x - 21)/(x + 3).
- 22nd March 1999y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 36.
- 23rd March 1999In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 24th March 1999The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 25th March 1999On 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?
- 26th March 1999Rationalise the denominator of 66/sqrt(11), giving your answer in its simplest form.
- 27th March 1999In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 28th March 1999A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 29th March 1999In a vector proof you find that vector PQ = 4a + b and vector RS = 12a + 3b. What does this show about PQ and RS?
- 30th March 1999A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 31st March 1999A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?