Daily Practice · Higher Plus
July 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1998y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 16.
- 2nd July 1998In a vector proof you find that vector PQ = 3a - 5b and vector RS = 6a - 10b. What does this show about PQ and RS?
- 3rd July 1998A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 4th July 1998On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th July 1998x = 150 and y = 85, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th July 1998Work out the nth term of the quadratic sequence 11, 24, 43, 68, ...
- 7th July 1998A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 8th July 1998A cuboid measures 12 cm by 13 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th July 1998A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th July 1998A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 11th July 1998A car covers 320 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th July 1998The point (2, 1) lies on y = f(x). Write down its image on y = f(x - 2).
- 13th July 1998y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 14th July 1998A cuboid measures 11 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th July 1998A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th July 1998On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th July 1998Rationalise the denominator of 6/sqrt(2), giving your answer in its simplest form.
- 18th July 1998Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 19th July 1998y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 20th July 1998The 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.
- 21st July 1998A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 22nd July 1998A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 23rd July 1998Simplify sqrt(50) + sqrt(32), giving your answer in the form a sqrt(b).
- 24th July 1998f(x) = 5x - 2 and g(x) = 3x + 4. Work out fg(-1).
- 25th July 1998y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 25.
- 26th July 1998In 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.
- 27th July 1998The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?
- 28th July 1998On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 29th July 1998A rectangle is 26 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th July 1998The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 31st July 1998A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.