Daily Practice · Higher Plus
September 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 1998 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1998A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 2nd September 1998On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd September 1998Simplify sqrt(18) + sqrt(18), giving your answer in the form a sqrt(b).
- 4th September 1998In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 5th September 1998y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 6th September 1998A cuboid measures 7 cm by 10 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th September 1998A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th September 1998A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 9th September 1998A rectangle is 9 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th September 1998Make x the subject of 8x + 8 = y(x + 8).
- 11th September 1998y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 25.
- 12th September 1998A cuboid measures 10 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th September 1998A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th September 1998On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th September 1998Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 16th September 1998Write 7/(x + 5) + 4/(x - 6) as a single fraction.
- 17th September 1998A train slows steadily from 28 m/s to rest in 10 seconds. Work out its deceleration.
- 18th September 1998The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 19th September 1998A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 20th September 1998A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 21st September 1998A block has mass 820 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd September 1998Solve 8x^2 - 10x - 25 = 0.
- 23rd September 1998y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 24th September 1998In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 25th September 1998The probability of winning a game is 1/4. A player expects 12 wins. How many games did they play?
- 26th September 1998On 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?
- 27th September 1998x = 143 and y = 57, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th September 1998f(x) = 2x + 2. Work out the inverse function f^-1(x).
- 29th September 1998y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 30th September 1998In a vector proof you find that vector PQ = 4a + b and vector RS = 8a + 2b. What does this show about PQ and RS?